"""
DaoMath Type System (道数类型系统)
基于 ±0 的类型理论
"""

from typing import TypeVar, Generic, Protocol, runtime_checkable
from dataclasses import dataclass
from enum import Enum


# ============================================================================
# 基础类型等级
# ============================================================================

class TypeLevel(Enum):
    """类型层级"""
    VOID = 0        # 空类型 ⊥
    INNATE = 1      # 先天类型 ±0
    DUAL = 2        # 对偶类型 {A, ¬A}
    TERNARY = 3     # 三元类型 {⊕, ⊖, ⊙}
    EMERGENT = 4    # 涌现类型


# ============================================================================
# 先天类型 (Innate Types)
# ============================================================================

@dataclass(frozen=True)
class InnateType:
    """
    先天类型: 基于 ±0 的类型
    
    所有类型最终归约到先天均衡态
    """
    positive_component: type
    negative_component: type
    neutral_component: type
    
    def __repr__(self) -> str:
        return f"±0⟨{self.positive_component.__name__}, {self.negative_component.__name__}, {self.neutral_component.__name__}⟩"


# ============================================================================
# 对偶类型 (Dual Types)
# ============================================================================

T = TypeVar('T')
U = TypeVar('U')

@dataclass(frozen=True)
class DualType(Generic[T]):
    """
    对偶类型: T ⊕ ¬T
    
    任意类型T都有其对偶¬T
    """
    primary: T
    dual: T
    
    def swap(self) -> 'DualType[T]':
        """交换对偶"""
        return DualType(primary=self.dual, dual=self.primary)


# ============================================================================
# 三元类型 (Ternary Types)
# ============================================================================

@dataclass(frozen=True)
class TernaryType(Generic[T]):
    """
    三元类型: {⊕, ⊖, ⊙}
    
    三种状态的统一
    """
    creation: T     # ⊕
    annihilation: T # ⊖
    conservation: T # ⊙


# ============================================================================
# 涌现类型 (Emergent Types)
# ============================================================================

@dataclass(frozen=True)
class EmergentType(Generic[T, U]):
    """
    涌现类型: T ⟹ U
    
    从类型T涌现出类型U
    """
    base_type: type[T]
    emergent_type: type[U]
    emergence_rule: callable


# ============================================================================
# 类型类 (Type Classes)
# ============================================================================

@runtime_checkable
class Balanced(Protocol):
    """可均衡类型"""
    def balance(self) -> InnateType:
        ...


@runtime_checkable
class Dualisable(Protocol):
    """可对偶类型"""
    def dual(self: T) -> T:
        ...


@runtime_checkable
class Conserved(Protocol):
    """守恒类型"""
    def conserved_quantity(self) -> float:
        ...


# ============================================================================
# 类型构造器
# ============================================================================

class TypeConstructor:
    """类型构造器"""
    
    @staticmethod
    def make_innate(pos_type: type, neg_type: type, neu_type: type) -> InnateType:
        """构造先天类型"""
        return InnateType(
            positive_component=pos_type,
            negative_component=neg_type,
            neutral_component=neu_type
        )
    
    @staticmethod
    def make_dual(value: T) -> DualType[T]:
        """构造对偶类型"""
        if isinstance(value, (int, float)):
            return DualType(primary=value, dual=-value)
        elif isinstance(value, bool):
            return DualType(primary=value, dual=not value)
        else:
            raise TypeError(f"Cannot create dual for type {type(value)}")
    
    @staticmethod
    def make_ternary(creation: T, annihilation: T, conservation: T) -> TernaryType[T]:
        """构造三元类型"""
        return TernaryType(
            creation=creation,
            annihilation=annihilation,
            conservation=conservation
        )


# ============================================================================
# 类型推导
# ============================================================================

class TypeInference:
    """类型推导引擎"""
    
    @staticmethod
    def infer_balance_type(value) -> InnateType:
        """推导平衡类型"""
        if isinstance(value, (int, float)):
            if value > 0:
                return InnateType(type(value), type(None), type(None))
            elif value < 0:
                return InnateType(type(None), type(value), type(None))
            else:
                return InnateType(type(None), type(None), type(value))
        else:
            return InnateType(type(value), type(value), type(value))
    
    @staticmethod
    def infer_dual_type(value) -> DualType:
        """推导对偶类型"""
        return TypeConstructor.make_dual(value)


# ============================================================================
# 使用示例
# ============================================================================

if __name__ == "__main__":
    print("=== 法则数学类型系统示例 ===\n")
    
    # 1. 先天类型
    print("1. 先天类型:")
    innate = TypeConstructor.make_innate(int, int, type(None))
    print(f"   {innate}\n")
    
    # 2. 对偶类型
    print("2. 对偶类型:")
    dual_num = TypeConstructor.make_dual(5)
    print(f"   数值对偶: {dual_num}")
    dual_bool = TypeConstructor.make_dual(True)
    print(f"   逻辑对偶: {dual_bool}\n")
    
    # 3. 三元类型
    print("3. 三元类型:")
    ternary = TypeConstructor.make_ternary(
        creation=lambda x: x + 1,
        annihilation=lambda x: x - 1,
        conservation=lambda x: x
    )
    print(f"   {ternary}\n")
    
    # 4. 类型推导
    print("4. 类型推导:")
    inferred = TypeInference.infer_balance_type(42)
    print(f"   42 → {inferred}")
    inferred = TypeInference.infer_balance_type(-3.14)
    print(f"   -3.14 → {inferred}")
